Van der Waals interactions with soft interfaces

Many naturally occurring microbiological and synthetic polymer systems have soft interfaces due, e.g., to the presence of polymer brushes at the surfaces. The initial interactions (before contact) in such systems are typically physical rather than chemical in origin, e.g. electrostatic or van der Waals forces. We calculate the form of the summed van der Waals interaction energies UHS and USS between two bulk systems separated by a distance D, when one (UHS) or both (USS) of their surfaces are soft. We find that the summed interactions diverge weakly as D → 0, UHS ∼ −1/D and USS ∼ − n(1/D), and comment upon the applicability of these results.